Three-dimensional unmanned aerial vehicle path planning using modified wolf pack search algorithm

Abstract

The unmanned aerial vehicle (UAV) has been a research focus in recent years. The path planner is a key element of the unmanned aerial vehicle autonomous control module. In this paper, the modified wolf pack search (WPS) algorithm is applied to compute the quasi-optimal trajectories for the rotor wing UAVs in the complex three-dimensional (3D) spaces including the real and fake 3D spaces. Moreover, it adopts the multi-objective cost function. In the path planning process, some concepts in the genetic algorithm (GA) are applied to realize the WPS algorithm. Then, the crossover and mutation operators in the GA method are introduced to improve the original WPS algorithm. Considering the dynamic properties of the vehicle, the path smoothing process based on the cubic B-spline curve is used to make the planning path suitable for the fixed wing UAVs. Simulation results show that this approach is efficient for the rotor wing UAVs and the fixed wing UAVs when taking into account of all kinds of constraints and the path generated is flyable. Moreover, the comparisons of the four algorithms show that the trajectories produced by the modified WPS algorithm are far superior to the original WPS algorithm, the GA and the random search way under the same conditions.

Introduction

The Unmanned Aerial Vehicle (UAV) path planning has become one of the most important elements to define a UAV mission. It allows the UAV to autonomously compute the best path from a start point to a target based on the task requirements and restraints. With the extensive use of various types of UAVs, the topic has attained a high popularity in recent years.

Various methods have been raised to deal with the UAV path planning problem, such as artificial potential field (APF) method [1], A* algorithm [2], genetic algorithm (GA) [3], artificial intelligence algorithms [4], [5] and so on. They can be segmented into traditional optimizing methods, computational intelligence methods and non-optimal algorithms. Most of these methods can solve the path planning problems effectively in general planning space.

The traditional optimizing methods include the APF method, the mixed-integer linear programming (MILP) method, the optimal control method and so on. Essentially, the APF method is based on the gradient method. This traditional method has been improved in the last several years. The authors introduced the airborne communication relay approach and the harmonic functions into the APF method for the autonomous UAVs path planning [6]. But the APF method has its own obvious deficiency. The main concern in the potential field methods is how to choose such a navigation function in order to avoid the vehicle being trapped in a local minimum. The MILP method is widely used in many areas of science, and it has been applied in the UAV path planning problem [7,8]. Since the integer programming, in general, is an NP-hard (non-deterministic polynomial-time hard) problem, the solution to the MILP optimization problem is not necessarily unique [9]. Similarly, the optimal control method is also a universal method [10]. Not only it is used in the UAV path planning problem, but also it can be applied in the UAV trajectory planning problem [11]. But the optimal control problem is very difficult to solve in most situations.

In general, the traditional optimizing methods are easily trapped into the local minimum. And there also exists the problem that they lack sufficient robustness. So the computational intelligence methods become more and more popular in the UAV path planning problem. The authors in [3] used the GA to solve the multi-constraints 3D UAV path planning problem. The authors of [5] compare the parallel GA with the parallel PSO algorithm in the real-time 3D path planning problem. The authors in [12] develop an anytime algorithm using the particle swarm optimization to solve the multiple UAV path planning problem. The authors of [13] presented two types of path planners based on the evolutionary algorithm in the on-line and off-line situation. Although the most computational intelligence methods have a powerful ability of global optimization, the efficiencies of the different methods are uneven for the same problem. So the efficiency is a very important index to measure an algorithm is good or bad.

The non-optimal algorithm is the generic terms of many different methods, includes the A* method, the Voronoi diagrams approach [14], the rapidly-exploring random tree (RRT) approach [15], the partially observable Markov decision processes (POMDP) and some other heuristic algorithms. The A* method and Voronoi diagrams approach are the graph-based algorithms. Importantly, the RRT approach is very popular in the UAV path planning area [13], [15], [16]. There are a series of papers and books focused on this approach. For example, the authors in [16] introduced an anytime algorithm based on a novel RRT* algorithm (like the RRT) which can converge to an optimal solution. In addition, a novel path-planning algorithm based on the POMDPs is presented recently. The authors of [17], [18] design a path-planning algorithm to guide the UAVs for tracking multiple ground targets based on the POMDPs.

Because the single method has its own inherent shortage, there are more and more researchers using the hybrid algorithm which integrates two or more methods to get a better planning result. For example, the authors put forward a novel algorithm combining the APF method with the GA for the robot path planning and the obstacle-avoidance [19].

The idea of the wolf pack search algorithm is first presented by the authors in [20]. They give a new algorithm, the wolf pack search-marriage in honey bees optimization (WPS-MBO) which introduces the WPS algorithm into the local search process of Marriage in Honey Bees Optimization algorithm [21]. At the same time, the definition of the WPS algorithm is proposed. The WPS algorithm is a swarm-intelligence method that imitates the arrest activity of a wolf group. Some popular complex Evaluation Functions and Traveling Salesman Problem (TSP) are successfully solved by the WPS algorithm. Importantly, its convergence performance is better than some other swarm-intelligence methods.

However, in the field of the complex 3D path planning for the UAV, no application of the WPS algorithm exists yet. In our paper, an original WPS algorithm and an improved WPS algorithm are used to solve the 3D UAV path planning problem. The concept of the GA chromosome is introduced to describe the meaning of the wolf in the path planning problem. Each wolf means an inherent chromosome and a possible path during the whole solution. The chromosome is the main operation object of the WPS algorithm. Especially, the environment description and the encoding of the chromosome are the major part of the solution process. After that stage has been overcome, the original WPS algorithm consists of the following steps: 1) Initialization – an initial wolf pack; 2) Fitness – evaluate the cost functions of the whole pack; 3) Elitism – select a more appropriate small group in the pack; 4) Safari – optimization in a small scale; 5) Update – every wolf gets close to the best wolf; 6) Replacement – replace old weak wolves by new ones; 7) Loop – go back to step 2 [22]. Of course, the whole circulation will stop if an end condition is satisfied, otherwise, it will continue. Here, the crossover and mutation operations in the GA method are added between Step 5 and Step 6 to propose a new metaheuristic algorithm according to the principle of the WPS algorithm, and then the improved WPS algorithm is used to search the optimal or suboptimal path in the planning space.

Therefore, it is observed that the processes of the original and modified WPS algorithm are both random and heuristic. Essentially, the original WPS algorithm is a random multi-initial values gradient algorithm, and it also has the characteristics included the parallel computing ability and the micro-region search capacity. So the original WPS algorithm characterizes with the good global search ability and the strong convergence ability. The original WPS algorithm is based on the relation between the best wolf and other common wolves. Therefore, the wolf pack is excessively dependent on the elitism. The connections of each two wolves are insufficient. By the help of the crossover and mutation operations, the relations among the whole wolf pack are introduced into the modified WPS algorithm. Therefore, the modified WPS algorithm has all advantages of the original WPS algorithm. At the same time, it also includes some new idea.

The general framework of this paper is as follows: firstly, the representations of the obstacles are statically defined. Then, the optimal path is computed off-line and it is properly smoothed. Finally, the UAV can move in the space according to the computed path.

The structure of this paper is as follows: In Section 2, the environment description models of the UAV path planning problem consider two different spaces. The encoding of the chromosome involving the genes and the structure of the chromosome and the multi-objective cost function of the chromosome are presented. Then, the whole optimization model of the path planning problem is established. In Section 3, the original WPS algorithm is introduced and applied to solve the problem. In Section 4, the improved WPS algorithm with the crossover and mutation operations for UAV is presented. The path smoothing which is the follow-up work of the UAV path planning problem is solved by the cubic B-spline curve in Section 5. At last, the simulation work and the further discussion are accomplished in Section 6.